Sigma-Algebra (σ-algebra)
★★★★☆Undergraduate
📖Definition
Collection of sets closed under complement and countable union. Structure for defining measures
📐Formulas
1. Ω ∈ Σ
2. A ∈ Σ ⇒ A^c ∈ Σ
3. A₁, A₂, ... ∈ Σ ⇒ ∪Aₙ ∈ Σ
✏️Examples
예제 1
Borel σ-algebra B(ℝ)
예제 2
{∅, Ω}
예제 3
Power set P(Ω)
⚡Applications
Probability
Integration
Functional analysis
🔗Related Documents
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